Geodesic
The Haagerup problem on subadditive weights on $W^*$-algebras
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2011), pp. 94-98

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In year 1975 U. Haagerup posed the following question: Whether every normal subadditive weight on a $W^*$-algebra is sigma-weakly lower semicontinuous? Here we positively answer this question in a particular case of abelian $W^*$-algebras and present a general form of normal subadditive weights on these algebras.
Keywords: $C^*$-algebra, $W^*$-algebra, subadditive weight, measurable function. 
@article{IVM_2011_10_a10,
     author = {A. M. Bikchentaev},
     title = {The {Haagerup} problem on subadditive weights on $W^*$-algebras},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {94--98},
     publisher = {mathdoc},
     number = {10},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2011_10_a10/}
}
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A. M. Bikchentaev. The Haagerup problem on subadditive weights on $W^*$-algebras. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2011), pp. 94-98. http://geodesic.mathdoc.fr/item/IVM_2011_10_a10/